Nonlinear oscillations in power systems have been extensively studied over the last years, to analyze and to determine their effects on the network. For that purpose, and based on analytical methodologies, normal forms of vector fields and modal series have been developed as a numerical tool, which allows the dynamic analysis of nonlinear systems. In this work, both methods are applied to analyze oscillations in two nonlinear systems. Observed differences between both methods are pointed out mainly those introduced by wrong selection of initial conditions. Time domain responses of a dynamical system used as a benchmark are analyzed in order to show this situation. Besides, a nine bus, three machines system is simulated to compare both nonlinear methodologies with respect to the numerical solution obtained with the direct solution of ordinary differential equations. The main differences observed between both methodologies when the power system is operated under a small perturbation and stress conditions are remarked.

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This document presents a robust control H∞ based in Linear Matrix Inequalities applied to a power multimachine interconnected system, which is expressed such as Differential and Algebraic linear model. The strategy permits to damp oscillations generated by changes in operation point of each subsystem and input perturbations in mechanic power. The strategy only uses minimal available information in output static feedback form. The feedback variables are local and remote for each machine. The control law is probed in a matlab/simulink simulated three machines benchmark. The simulations and the results are showed at the end of paper.